Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
Likelihood Estimation for Stochastic Epidemics with Heterogeneous Mixing Populations

Authors: Yilun Shang

Abstract:

We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem.

Keywords: statistic inference, maximum likelihood, epidemicmodel, heterogeneous mixing.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333598

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1052

References:


[1] P. K. Andersen, ├ÿ. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes. Springer, New York, 1993
[2] H. Andersson, Epidemic models and social networks. Math. Scientist, 24(1999) 128-147
[3] H. Andersson and T. Britton, Stochastic Epidemic Models and Their Statistical Analysis. Springer-Verlag, New York, 2000
[4] N. T. J. Bailey, The Mathematical Theory of Infectious Diseases and Its Application. Griffin, London, 1975
[5] F. G. Ball and O. D. Lyne, Stochastic multitype SIR epidemics among a population partitioned into households. Adv. Appl. Prob., 33(2001) 99-123
[6] F. Ball, D. Mollison and G. Scalia-Tombra, Epidemics with two levels of mixing. Ann. Appl. Probab., 7(1997) 46-89
[7] F. Brauer and J. Watmough, Age of infection epidemic models with heterogeneous mixing. J. Biol. Dyn., 3(2009) 324-330
[8] T. Britton, T. Kypraios and P. D. O-Neill, Statistical inference for stochastic epidemic models with three levels of mixing. arXiv:0908.2066v1
[stat.AP], 2009
[9] T. Britton and P. D. O-Neill, Bayesian inference for stochastic epidemics in popluations with random social structure. Scand. J. Statist., 29(2002) 375-390
[10] N. Demiris and P. D. O-Neill, Bayesian inference for epidemics with two levels of mixing. Scand. J. Statist., 32(2005) 265-280
[11] N. Demiris and P. D. O-Neill, Bayesian inference for stochastic multitype epidemics in structured populations via random graphs. J. Roy. Statist. Soc. Ser. B, 67(2005) 731-746
[12] S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence. Wiley, New York, 1986
[13] W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics. Proc. Roy. Soc. London Ser. A, 115(1927) 700-721
[14] R. Rebolledo, Central limit theorems for local martingales. Z. Wahrsch. Verw. Gebiete., 51(1980) 269-286
[15] W. N. Rida, Asymptotic properties of some estimators for the infection rate in the general stochastic epidemic model. J. R. Statist. Soc. B, 53(1991) 269-283